Bistable limit cycle oscillations in chemical systems. I. Basins of attraction

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When bistable oscillations occur in nonlinear chemical systems, the concentration space can be separated into regions that asymptotically tend to each of the oscillatory states. The structure of such basins of attraction is studied for Rössler’s model of a far-from-equilibrium chemical system. Starting with a set of local pictures of the basins, their three-dimensional structure is deduced. The idea of a phase basin is introduced. For a multilooped limit cycle, the phase basin is the set of those initial phase points that tend to the same discrete phase of the cycle, defined in a plane that cuts the cycle transversely. The nature of such basins of attraction is important for studies of noise-induced transitions between coexisting limit cycles or loss of phase coherence in a single limit cycle.